The present invention concerns editing images and pertains specifically to order dependent adjustments applied to a digitally represented image so that a consistent and predictable result ensues with strict provision for digital information losses.
When an adjustment is applied to a digitally represented image, information contained in digital representation may be lost. For example, one operation might be to reduce the brightness. When brightness is adjusted, the internal values for brightness are lowered for each pixel. Internally, pixels are represented by numerical values that are whole numbers. Typically, fractional information is not saved when whole number representations are changed. This means that ratios of the brightness values between any two pixels will usually change as a result of an adjustment in brightness. This represents a non-recoverable loss of information.
In the digital domain, the operation "reduce brightness by the fraction (x/y)" results in pixels whose resulting brightness components are fractions being rounded to whole digits. Likewise, in the digital domain, the operation "increase brightness by the fraction (y/x)" can result in pixels whose resulting brightness components are fractions being rounded to whole digits. Thus in the digital domain, performing the operation "reduce brightness by the fraction (x/y)" followed by the operation "increase brightness by the fraction (y/x)" results in a loss of information. Performing these operations in sequential order in the digital domain can thus result in a loss of information, while performing the same operation in an analog or continuous domain could result in significantly less loss of information.
For example, suppose that a given pixel had an initial brightness value of 126, and that x equals 3 and y equals 10. The ratio (x/y) is then equal to 0.30. The operation "reduce brightness by the fraction (x/y)" results in the brightness value of 37.8 in the analog domain, but 38 in the digital or whole number domain, with rounding to the nearest integer. Trying to reverse this operation by increasing the brightness to y/x (10/3) or 3.3333, results in a new brightness value of 38*10/3=126.666 or 127 when rounded up in the digital domain. Thus in the digital domain, these two sequential operations result in an error of 1 unit of brightness. Because of the lost information, digital operations, even though theoretically reversible, can result in lost information and incorrect results.
Further, if after adjusting the brightness in the digital domain, additional adjustments are made, such as changing the contrast or changing the dynamic range of the pixels, to the image representation, whichever adjustment is performed first affects the errors on subsequent adjustments. The results will be different for different sequential orderings of the adjustments on the digitally represented image.